Mixed-mode Fracture Toughness Research Articles

Effects of Microstructure and Loading on Fracture of Sn-3.8Ag-0.7Cu Joints on Cu Substrates with ENIG Surface Finish

When dropped, electronic packages often undergo failure by propagation of an interfacial crack in solder joints under a combination of tensile and shear loading. Hence, it is crucial to understand and predict the fracture behavior of solder joints under mixed-mode high-rate loading conditions. In this work, the effects of the loading conditions (strain rate and loading angle) and microstructure interfacial intermetallic compound (IMC) morphology and solder yield strength] on the mixed-mode fracture toughness of Sn-3.8 wt.%Ag-0.7 wt.%Cu solder joints sandwiched between two Cu substrates with electroless nickel immersion gold (ENIG) metallization have been studied, and compared with the fracture behavior of joints attached to bare Cu. Irrespective of the surface finish, the fracture toughness of the solder joints decreased monotonically with strain rate and mode-mixity, both resulting in increased fracture proportion through the interfacial IMC layer. Furthermore, the proportion of crack propagation through the interfacial IMC layer increased with increase in the thickness and the roughness of the interfacial IMC layer and the yield strength of the solder, resulting in a decrease in the fracture toughness of the joint. However, under most conditions, solder joints with ENIG finish showed higher resistance to fracture than joints attached directly to Cu substrates without ENIG metallization. Based on the experimental observations, a fracture mechanism map is constructed correlating the yield strength of the solder, the morphology and thickness of the interfacial IMC, and the fracture mechanisms as well as the fracture toughness values for different solder joints under mode I loading.

A general methodology for calculating mixed mode stress intensity factors and fracture toughness of solder joints with interfacial cracks

Solder joints in electronic packages undergo thermo-mechanical cycling, resulting in nucleation of micro-cracks, especially at the solder/bond-pad interface, which may lead to fracture of the joints. The fracture toughness of a solder joint depends on material properties, process conditions and service history, as well as strain rate and mode-mixity. This paper reports on a methodology for determining the mixed-mode fracture toughness of solder joints with an interfacial starter-crack, using a modified compact mixed mode (CMM) specimen containing an adhesive joint. Expressions for stress intensity factor (K) and strain energy release rate (G) are developed, using a combination of experiments and finite element (FE) analysis. In this methodology, crack length dependent geometry factors to convert for the modified CMM sample are first obtained via the crack-tip opening displacement (CTOD)-based linear extrapolation method to calculate the under far-field mode I and II conditions (f1a and f2a), (ii) generation of a master-plot to determine ac, and (iii) computation of K and G to analyze the fracture behavior of joints. The developed methodology was verified using J-integral calculations, and was also used to calculate experimental fracture toughness values of a few lead-free solder-Cu joints.

Mixed-mode fracture toughness of bond lines of PRF and PUR adhesives in European beech wood

Abstract The fracture behavior of bond lines in hardwood has been studied. The joints of a phenol resorcinol formaldehyde (PRF) resin and a one-component polyurethane (PUR) adhesive with European beech wood (Fagus sylvatica L.) adherends were examined for their fracture toughness (K c). The initial crack tip was placed directly in the adhesive as a thin silicon film. Thereby, the examination of the bond line, and not the solid wood, can be assured. Five different load angles were applied, from fracture mode 1 (M1) to mode 2 (M2), with an Arcan test mount. Additionally, three sample series conditioned at the relative humidities (RH) of 50%, 65%, and 95% of the surrounding air were tested. The results clearly show an increasing K c of both adhesives with increasing shear stresses. This observation is valid for all RHs, but the differences decrease with increasing RH. The moisture dependency is more pronounced in PUR than in PRF glue joints. PUR generally shows a lower K c than PRF, with the only exceptions being K I,c and K II,c in dry climate. The subsequent crack propagation in the PRF samples mainly takes place in the wood adherend, whereas, in the PUR samples, the cracks remain within the bond line (adhesive failure). Nevertheless, the performance of PUR glue joints is not worse than that of the solid wood, which can be attributed to the ductile behavior of the adhesive.

The notch effect on fracture of polyurethane materials

This paper investigates the fracture properties and notch effect of PUR materials with four different densities. The asymmetric semi-circular bend specimen was adapted to perform mixed mode fracture toughness tests. This semi-circular specimen with radius R, which contains an edge crack of length a oriented normal to the specimen edge, loaded with a three point bending fixture, was proved to give wide range of mixed modes from pure mode I to pure mode II, only by changing the position of one support. Different types of notched specimens were considered for notch effect investigations and the Theory of Critical Distances was applied. It could be seen that the critical distances are influenced by the cellular structure of investigated materials.

On fracture of kinked interface cracks – The role of T-stress

This paper presents a modified maximum tangential stress criterion (MMTS) for prediction of the fracture initiation conditions in kinked bi-material cracks. The criterion takes into account the effect of T-stress as well as the stress intensity factors (KI and KII) to predict the mixed mode fracture toughness of interface cracked specimens. First the fracture criterion is developed and the effect of sign and magnitude of T-stress on mixed mode fracture toughness is studied analytically. Then, the suggested criterion is evaluated using the experimental data reported for some epoxy/Aluminum Brazil-nut-sandwich specimens in the literature. The MMTS criterion is also compared with the conventional maximum tangential stress (MTS) criterion and hence, significantly improved estimates were achieved for mixed mode fracture toughness of the tested specimens.

Effects of temperature and confining pressure on mixed-mode (I–II) and mode II fracture toughness of Kimachi sandstone

1. IntroductionFracture mechanics is becoming increasingly important insolving problems relating to rock strength in mining engineeringand civil engineering. For example, fracture mechanics can be usedfor the design of hydraulic fracturing for geothermal energy, oiland natural gas recovery [1–4], as well as for the analysis of rockmass stability in slopes or those associated with excavations [5,6],and determining rock fragmentation by blasting or in the event ofrock burst [7,8].Therefore, it is desirable to investigate the fracture toughness,which is an important rock property that characterizes its fracturebehavior. In this investigation, fracture toughness was determinedat elevated pressures and temperatures simulating the conditionsprevailing underground. A number of test specimen configurationsand methods have been suggested to determine the fracturetoughness of rock materials. The International Society for RockMechanics (ISRM) has incorporated the chevron-notched bendspecimen [9], the short rod specimen [10] and cracked chevron-notched Brazilian disc (CCNBD) specimen [11] into the standardmethod for measurement of the fracture toughness of rock. Thesemi-circular bend (SCB) specimen proposed in [12,13] is com-plementary to the standard method (Fig. 1).Natural crack propagation occurs as a result of the develop-ment and coalescence of tensile and shear cracks. The geometryand loading are defined as mode I (tensile mode), mode II(in-plane shear), mode III (anti-plane shear) crack propagation,and mixed modes of mode I, II, and III. Previous studies on thefracture toughness of rock were mostly focused on mode I crackpropagation. However, actual crack propagation in rock massoccurs not only in tensile mode but also as part of in-plane shearmode. Mode II fracture toughness and the critical stress intensityfactors in mixed mode (I–II) are crucial to gain understanding intorock fracturing. SCB specimen and Cracked Straight ThroughBrazilian Disc (CSTBD) specimen [14] have been used for evaluat-ing mode II and mixed mode fracture toughness of rock, and thePunch-Through Shear test (PTS) specimen [15] has been developedto evaluate mode II fracture toughness of rock. Furthermore, thePTS specimen is adopted as an ISRM suggested method. Conse-quently, many researchers have investigated the mixed mode (i.e.mode I and mode II) and pure mode II fracture toughness of rock[16–23]. In terms of the ratio of mode II fracture toughness, K

Study of characteristic specification on mixed mode fracture toughness of asphalt mixtures

Low temperature cracking is one of the main deterioration and failure modes for pavements. Hence, in this paper the effect of asphalt characteristic on its mixed mode I/II low temperature fracture toughness is investigated experimentally. A large number of edge cracked semi circular bend specimens subjected to asymmetric three-point bend loading were tested for different hot mix asphalt mixtures made of various compositions. The influence of aggregate type and size, binder type and air void content were studied on the critical stress intensity factors of four mode mixtures ranging from pure mode I to pure mode II. The fracture toughness results showed the noticeable influence of asphalt characteristic specifications on the low temperature cracking behaviour of mixtures subjected to mixed mode loading.

To Improve Mixed-Mode Interlaminar Fracture Toughness of Composite Sub-Structures

The present paper investigates the influence of stitching on delamination resistance of laminated composite structures. The mixed-mode interlaminar fracture toughness, GI/IIC, of the stitched hybrid laminated composites is studied in order to investigate the resistance of the 3D-composites to the crack propagation in delaminated composite structures. To that end, the mixed-mode interlaminar fracture toughness was measured using the asymmetric double cantilever beam (ADCB) test method. The hybrid ADCB and stitched hybrid ADCB composite beams were laid-up in order to study the effect of stitching on the interlaminar fracture toughness. The test results showed that the resistance of stitched fibres against the crack propagation in stitched hybrid composites can significantly improve the mixed-mode interlaminar fracture toughness.

Mixed Mode Interlaminar Fracture of Carbon Nanotubes Enhanced Epoxy/Glass Fiber Composites

Present paper studied the improvement of the fracture toughness under mixed mode loading obtained by using carbon nanotubes reinforcement in fiber glass mats/ epoxy laminates. Mixed-mode bending tests were performed considering different loading ratios GII/GI. Laminates were manufactured using the epoxy resin Biresin® CR120 reinforced with fiber glass triaxial mats ETXT 450 and multiwalled carbon nanotubes with 98% of carbon. It was observed that the total fracture toughness increases linearly with the mode II loading component and that linear mixed-mode fracture criteria reproduces the GI versus GII relationship. The incorporation of small quantity, up to 0.5%, of carbon nanotubes into matrix improves significantly mixed-mode fracture toughness.

A Study of Rock Crack Fracture under Different Temperatures

A series of critical fracture toughness of two kinds of rock materials under different temperature which varied from-50°C to 240°C are measured by I-II-III mixed mode fracture experiments adopting atypical three point bending specimens. Relative stress intensity factors of crack initiation are calculated by finite element method. Combining with calculated values, the experiment results show that, the mixed mode fracture toughness of the rocks decreases with the increase of temperature. The experimental and calculated results can be used in the design of deep underground engineering or disaster prevention and mitigation engineering.

Experimental Investigation of the Interface Behavior of Balanced and Unbalanced E-Glass/Polyester Woven Fabric Composite Laminates

The aim of this work is to study the influence of weave structure on the crack growth behavior of thick E-glass/polyester woven fabric composites laminates. Two different types of laminates were fabricated: (i) balanced: plain weave (taffetas T)/chopped strand mat weave (M) [T/M]6 and (ii) unbalanced: 4-hardness satin weave (S)/chopped strand mat weave [S/M]7. In order to accurately predict damage criticality in such structures, mixed mode fracture toughness data is required. So, the experiments were conducted using standards delamination tests under mixed mode loading and pure mode loading. These tests were carried out in mode II using End Load Split (ELS) tests and in mixed-mode I+II by Mixed Mode Flexure (MMF) tests under static conditions. The test methodology used for the experiments will be presented. The experimental results have been expressed in terms of total strain energy release rate and R-curves. The fracture toughness results show that the T/M interface is more resistant to delamination than the S/M interface.

Sudden Fracture from U-Notches in Fine-Grained Isostatic Graphite Under Mixed Mode I/II Loading

The U-notched maximum tangential stress (UMTS) criterion, proposed originally and utilized previously by the author and his co-researcher for predicting mixed mode I/II fracture in plexi-glass (PMMA) and also pure mode II fracture in PMMA and soda-lime glass, was employed to estimate the experimental results reported in literature dealing with brittle fracture of many U-notched fine-grained isostatic graphite plates under combined tensile/shear loading conditions. By using the fracture curves of the UMTS criterion, which can predict the onset of brittle fracture in terms of the notch stress intensity factors (NSIFs) in the entire domain from pure mode I to pure mode II, the mixed mode fracture toughness (i.e. the load-bearing capacity) of U-notched graphite plates was successfully estimated.

An enhanced beam-theory model of the mixed-mode bending (MMB) test—Part I: Literature review and mechanical model

The paper presents a mechanical model of the mixed-mode bending (MMB) test used to assess the mixed-mode interlaminar fracture toughness of composite laminates. The laminated specimen is considered as an assemblage of two sublaminates partly connected by an elastic–brittle interface. The problem is formulated through a set of 36 differential equations, accompanied by suitable boundary conditions. Solution of the problem is achieved by separately considering the two subproblems related to the symmetric and antisymmetric parts of the loads, which for symmetric specimens correspond to fracture modes I and II, respectively. Explicit expressions are determined for the interfacial stresses, internal forces, and displacements.

Effect of prepreg storage humidity on the mixed-mode fracture toughness of a co-cured composite joint

The present work investigated the effect of the level of prepreg moisture content on the mixed-mode fracture toughness of a co-cured composite joint. It was found that moisture was stored in the prepreg as either free or bound water. It was also shown that the prepreg stores moisture from high humidity environments as free water, while the level of bound water remains unaffected. The excessive moisture was shown to plasticise the adhesive, lowering the glass transition temperature. The fracture toughness decreased under mode I and mode II loading as the humidity level was increased. There was a significant increase in mixed-mode toughness under low humidity conditions. Although the mixed-mode toughness reduced with increasing levels of humidity, the values never fell below that of the joints fabricated using the as-received materials.

Mixed-Mode Bending Test for Fracture Toughness of Composite Bonding Adhesive Layer

This paper describes the mixed-mode bending test fracture toughness of composite adhesive J116-b. The test theory and experimental requirements are introduced. The fracture toughness of mode I, mode II, and different mode mixture of 0.4, 0.6, and 0.8 are obtained. It is found that the total fracture toughness is increasing with the increasing of mode mixture. It is also obtained that the technique of calculating fracture toughness by considering the influence of the weight of lever and attach apparatus is more accurate.

An Experimental and Numerical Investigation of the Mixed-Mode Fracture Toughness and Lap Shear Strength of Aerospace Grade Composite Joints

In the present study, the mixed-mode fracture toughness of an adhesively bonded composite joint system was examined using a variety of linear elastic fracture mechanics (LEFM) based tests. These tests include the mode I double cantilever beam (DCB), mixed-mode asymmetrical DCB (ADCB) and mode II end load split (ELS) test. The joint system was also evaluated using the wide area lap shear (WALS) test that is often employed by the aerospace industry. While lap shear type tests are relatively simple to perform and post-process compared to their LEFM counterparts, the results can often be misleading and are greatly dependent on the overlap length, thickness of substrate and type of fillet. The experimental tests were also simulated using OpenFOAM, a finite volume based software package. Through this combined experimental-numerical approach, a greater understanding of the influence of the peel ply surface treatment and scrim cloth on the behaviour of the WALS test was achieved.

Experimental and Numerical Investigation of Mixed-Mode Interlaminar Fracture of Carbon-Polyester Laminated Woven Composite by Using Arcan Set-up

Composite materials are widely used in marine, aerospace and automobile industries. These materials are often subjected to defects and damages from both in-service and manufacturing process. Delamination is the most important of these defects. This paper reports investigation of mixed-mode fracture toughness in carbon–polyester composite by using numerical and experimental methods. All tests were performed by Arcan set-up. By changing the loading angle, α, from 0° to 90° at 15° intervals, mode-I, mixed-mode and mode-II fracture data were obtained. Correction factors for various conditions were obtained by using ABAQUS software. Effects of the crack length and the loading angle on fracture were also studied. The interaction j-integral method was used to separate the mixed–mode stress intensity factors at the crack tip under different loading conditions. As the result, it can be seen that the shearing mode interlaminar fracture toughness is larger than the opening mode interlaminar fracture toughness. This means that interlaminar cracked specimen is tougher in shear loading condition and weaker in tensile loading condition.

Typical Upper Bound–Lower Bound Mixed Mode Fracture Resistance Envelopes for Rock Material

Mixed mode fracture experiments were conducted on Harsin marble using two disc-shape samples namely the Brazilian disc (BD) and the semi-circular bend (SCB) specimens. For each specimen, a complete fracture toughness envelope ranging from pure mode I to pure mode II was obtained. The experimental results indicate that the mixed mode fracture toughness depends on the geometry and loading conditions such that for any similar mode mixture, the BD test data were significantly greater than the SCB fracture toughness results. Therefore, the conventional fracture criteria which present a unique mixed mode fracture curve, fail to predict the test results. It is shown that a generalized criterion, which takes into account the effects of geometry and loading conditions, is able to provide individual fracture curves for theses specimens with very good estimates for the test results obtained from both BD and SCB specimens. The BD and SCB specimens can be suggested as appropriate specimens for obtaining typical upper bound and lower bound envelopes for mixed mode fracture toughness of rocks.

Experimental and Numerical Investigation of Mixed-Mode Fracture Properties of Woven Laminated Composite

Delamination is a major problem associated with composite materials that reduce the stiffness of structure used in aerospace, marine and automotive technology. Interlaminar fracture toughness, non dimensional stress intensity factors and delamination crack growth behavior were investigated for carbon fiber (CF)-polyester laminates. All tests were performed with modified version of Arcan specimen. By changing the loading angles in range of 0-90°, mode-I, mode-II and all mixed mode fracture toughness data were obtained. Correction factors were obtained with finite element analysis using Abaqus software. By employing experimentally measured critical loads and the aid of the finite element method, mixed-mode fracture toughness for the composite under consideration determined. The fracture surfaces of the CF-P under different mixed-mode loading conditions were examined by optical and scanning electron microscopy (SEM) to gain insight into the failure responses.

Fracture characterization of Carbon fiber-reinforced polymer-concrete bonded interfaces under four-point bending

A combined analytical and experimental approach is presented to characterize both mode-II and mixed mode fracture of Carbon fiber-reinforced polymer-concrete bonded interfaces under four-point bending load, and closed-form solutions of compliance and energy release rate of the mode-II (four-point symmetric end-notched flexure) and mixed (four-point asymmetric end-notched flexure) mode fracture specimens are provided. The transverse shear deformation in each sub-layer of bi-material bonded beams is included by modeling each sub-layer as an individual first order shear deformable beam, and the effect of interface crack tip deformation on the compliance and energy release rate are taken into account by applying the interface deformable bi-layer beam theory (i.e., the flexible joint model). The improved accuracy of the present analytical solutions for both the compliance and energy release rate is illustrated by comparing with the solutions predicted by the conventional rigid joint model and finite element analysis. The fracture of Carbon fiber-reinforced polymer-concrete bonded interface is experimentally evaluated using both the four-point symmetric and asymmetric end-notched flexure specimens, and the corresponding values of critical energy release rates are obtained. Comparisons of the compliance rate-changes and resulting critical energy release rates based on the rigid joint model, the present theoretical model, and numerical finite element analysis demonstrate that the crack tip deformation plays an important role in accurately characterizing the mixed mode fracture toughness of hybrid material bonded interfaces under four-point bending load. The improved solution of energy release rates for the four-point symmetric and asymmetric end-notched flexure specimens by the flexible joint model can be used to effectively characterize hybrid material interface, and the fracture toughness values obtained for the Carbon fiber-reinforced polymer-concrete interface under mode-II and mixed mode loading can be employed to predict the interface fracture load of concrete structures strengthened with composites.